Question: Given $ m \angle CBD = 3x - 15$, $ m \angle ABC = 2x + 30$, and $ m \angle ABD = 80$, find $m\angle CBD$. $B$ $A$ $D$ $C$
Explanation: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Substitute in the expressions that were given for each measure: $ {2x + 30} + {3x - 15} = {80}$ Combine like terms: $ 5x + 15 = 80$ Subtract $15$ from both sides: $ 5x = 65$ Divide both sides by $5$ to find $x$ $ x = 13$ Substitute $13$ for $x$ in the expression that was given for $m\angle CBD$ $ m\angle CBD = 3({13}) - 15$ Simplify: $ {m\angle CBD = 39 - 15}$ So ${m\angle CBD = 24}$.